Ip, W. and Wong, H. and Pan, J. and Li, D.F.
(2006)
*The asymptotic convexity of the negative likelihood function of GARCH models.*
Computational Statistics and Data Analysis, 50 (2).
pp. 311-331.
ISSN 0167-9473

Official URL: http://dx.doi.org/10.1016/j.csda.2004.08.012

## Abstract

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH. A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign exchange rates is also given.

Item type: | Article |
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ID code: | 4931 |

Keywords: | GARCH, convexity, maximum likelihood estimation, iterative algorithm, convergence, foreign exchange rates, statistics, data analysis, Probabilities. Mathematical statistics, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics, Statistics and Probability |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 30 Nov 2007 |

Last modified: | 10 Dec 2015 17:15 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4931 |

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